How to calculate safety stock: formula and worked example

Safety stock is the buffer held against demand exceeding the forecast or the supplier delivering late. Too little and the shelf goes empty; too much and money sits in stock. The right amount depends on three things: how wrong the forecast is, how much the lead time varies and how much risk is acceptable.

Formula

σLT  = √( L × σd²  +  d² × σL² )
SS   = z × σLT

The first term under the root carries demand uncertainty (forecast error accumulated over the lead time), the second lead time uncertainty (if delivery is a day late, one more day of demand must be covered).

Service level and z

The service level is the probability of not running out in an order cycle.

Step-by-step example

A product sells 10 units a day on average. The standard deviation of the monthly forecast error is 60 units. The supplier delivers in 14 days on average, varying by ±3 days. The target service level is 95%.

1. Monthly error to daily:  σd  = 60 / √30.4375        = 10.875
2. Demand uncertainty:      L × σd²  = 14 × 10.875²    = 1,655.8
3. Lead time uncertainty:   d² × σL² = 10² × 3²        = 900
4. Total uncertainty:       σLT = √(1,655.8 + 900)     = 50.56
5. Safety stock:            SS  = 1.6449 × 50.56       = 83.2 units

The monthly error is converted to a daily one by dividing by the square root of the average days in a month (30.4375), assuming daily errors are independent. To try your own figures, use the safety stock calculator.

A notable result: if the ±3-day lead time variation were ignored, the safety stock would be 66.9 units. So that variation makes up about a fifth of the safety stock.

From safety stock to reorder point

Safety stock alone does not answer “when to order”. Adding the expected demand over the lead time gives the reorder point:

reorder point = d × L + SS = 10 × 14 + 83.2 = 223.2 units

An order is placed when stock on hand and on order falls to this point. See Reorder point.

Common mistakes

• The same number of days for everyone: a “15 days of safety stock for every product” rule leaves too much stock for well-forecast products and too little for erratic ones.
• Ignoring lead time variability: in the example above it understates safety stock by about 20% (66.9 instead of 83.2).
• Outdated parameters: if the supplier now delivers later, the lead time on the product card must be updated.
• Using the standard deviation of demand: gives too much safety stock for seasonal products; the forecast error should be used.

In VidiStock

VidiStock does this calculation for every product and warehouse: it takes the forecast error from backtesting, the lead time and its variability from the product card, and the service level from the product, warehouse or company setting. It warns when the actual lead time is clearly longer than the one on the product card. Every order suggestion has a breakdown window with these steps. Details: Methods and accuracy.